Games on graphs with ω-regular objectives provide a model for the control and synthesis of reactive systems. Every ω-regular objective can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens “eventually.” Two main strengths of the classical, infinite-limit formulation of liveness are robustness (independence from the granularity of transitions) and simplicity (abstraction of complicated time bounds). However, the classical liveness formulation suffers from the drawback that the time until something good happens may be unbounded. A stronger formulation of liveness, so-called finitary liveness, overcomes this drawback, while still retaining robustness and simplicity. Finitary liveness requires that there exists an unknown, fixed bound b such that something good happens within b transitions. While for one-shot liveness (reachability) objectives, classical and finitary liveness coincide, for repeated liveness (Büchi) objectives, the finitary formulation is strictly stronger. In this work we study games with finitary parity and Streett (fairness) objectives. We prove the determinacy of these games, present algorithms for solving these games, and characterize the memory requirements of winning strategies. Our algorithms can be used, for example, for synthesizing controllers that do not let the response time of a system increase without bound.
This research was supported in part by the AFOSR MURI grant F49620-00-1-0327 and the NSF ITR grant CCR-0225610.
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TACAS: Tools and Algorithms for the Construction and Analysis of Systems
Chatterjee K, Henzinger TA. Finitary winning in omega-regular games. In: Vol 3920. Springer; 2006:257-271. doi:10.1007/11691372_17
Chatterjee, K., & Henzinger, T. A. (2006). Finitary winning in omega-regular games (Vol. 3920, pp. 257–271). Presented at the TACAS: Tools and Algorithms for the Construction and Analysis of Systems, Springer. https://doi.org/10.1007/11691372_17
Chatterjee, Krishnendu, and Thomas A Henzinger. “Finitary Winning in Omega-Regular Games,” 3920:257–71. Springer, 2006. https://doi.org/10.1007/11691372_17.
K. Chatterjee and T. A. Henzinger, “Finitary winning in omega-regular games,” presented at the TACAS: Tools and Algorithms for the Construction and Analysis of Systems, 2006, vol. 3920, pp. 257–271.
Chatterjee K, Henzinger TA. 2006. Finitary winning in omega-regular games. TACAS: Tools and Algorithms for the Construction and Analysis of Systems, LNCS, vol. 3920. 257–271.
Chatterjee, Krishnendu, and Thomas A. Henzinger. Finitary Winning in Omega-Regular Games. Vol. 3920, Springer, 2006, pp. 257–71, doi:10.1007/11691372_17.